Revision: Chemical Kinetics Chemistry HSC Science (General) 12th Standard Board Exam Maharashtra State Board

The rate of a chemical reaction may be defined as the change in concentration of any of the reactants or any of the products per unit time.

Rate of Reaction = `"Change in concentration of a reactant or a prodect"/"Time taken for the change"`

The reactions that have higher order true rate law but are found to behave as first order are called pseudo first order reactions.

\[\ce{CH3COOCH3 + H2O - CH3COOH + CH3OH}\]

Zero order reaction is the reaction whose rate is independent of the reactant concentration and remains constant throughout the course of the reaction.

Half life of a reaction is defined as the time required for the reactant concentration to reach one half of its initial value.

The half-life t_1/2 is the time required for the concentration of a reactant to fall to half its initial value.

\[t_{1/2}\propto\frac{1}{[A_0]^{n-1}}\]

Activation energy is the lowest energy necessary to commence a chemical reaction by disrupting the bonds of reactant molecules and creating the activated complex or transition state. It signifies the energy threshold that must be surmounted for a reaction to transpire. Activation energy is typically represented as E_a.

Activation energy may be defined as the excess energy that the reactant molecules (having energy less than the threshold energy) must acquire in order to cross the energy barrier and to change into the products.

The Arrhenius equation is a mathematical expression to give a quantitative relationship between the rate constant and temperature.

\[\mathrm{Rate}=\frac{\text{Decrease in concentration of Reactant}}{\text{Time interval}}\]

\[=-\frac{\Delta[R]}{\Delta T}\]

\[\mathrm{Rate}=\frac{\text{Increase in concentration of Product}}{\text{Time interval}}\]

\[=+\frac{\Delta\left[P\right]}{\Delta T}\]

For a general reaction aA + bB → cC + dD:

\[\frac{dx}{dt}=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}\]

Collision Theory explains why and how temperature increases the rate of reaction.

Microscopic Factors:

Factor 1: Collisional Frequency (Z):

• The number of collisions taking place per second per unit volume of the reaction mixture.
• Effective collision: Only those collisions that actually produce the products.

\[\mathrm{Rate}=\frac{dx}{dt}=Z\times\text{(fraction of effective collisions)}\]

Factor 2: Activation Energy:

• The minimum amount of extra energy required by a reacting molecule to get converted into an activated molecule (transition state).
• Ea = Threshold energy − Average energy of reactant molecules

Conditions for Effective Collision:

1. Colliding molecules must possess energy ≥ threshold energy.
2. Colliding molecules must have proper orientation at the time of collision.

Drawback of Collision Theory: It considers atoms/molecules to be hard spheres and ignores their structural features.

The rate of a reaction depends on:

Temperature Coefficient:

The temperature coefficient μμ is the ratio of rate constants at two temperatures differing by 10°C:

\[\mu=\frac{k_{T+10}}{k_T}=2\mathrm{~to~3}\]

The two reference temperatures are typically 35°C (308 K) and 25°C (298 K).

If R₁​ = reaction rate at T₁​ and R₂​ = reaction rate at T₂​:

\[\frac{R_1}{R_2}=\frac{\mu T}{10}\]

Arrhenius Equation:

\[k=A\cdot e^{-E_a/RT}\]

where:

• k = rate constant
• A = pre-exponential factor (frequency factor)
• EaEa​ = activation energy (J mol⁻¹)
• R = gas constant (8.314 J mol⁻¹ K⁻¹)
• T = temperature in Kelvin

The factor \[e^{-E_a/RT}\] is called the Boltzmann factor.

Logarithmic form:

\[\log k=\log A-\frac{E_a}{2.303RT}\]

A plot of log k vs 1/T is a straight line with:

\[\mathrm{Slope}=-\frac{E_a}{2.303R}\]

Intercept = log A

This is of the form y = mx + c.

Two-Temperature Form:

\[\log\frac{k_2}{k_1}=\frac{E_a}{2.303R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)=\frac{E_a}{2.303R}\left(\frac{T_2-T_1}{T_1T_2}\right)\]